Summary• The deployment of resistant crops often leads to the emergence of resistance-breaking pathogens that suppress the yield benefit provided by the resistance. Here, we theoretically explored how farmers' main leverages (resistant cultivar choice, resistance deployment strategy, landscape planning and cultural practices) can be best combined to achieve resistance durability while minimizing yield losses as a result of plant viruses.• Assuming a gene-for-gene type of interaction, virus epidemics are modelled in a landscape composed of a mosaic of resistant and susceptible fields, subjected to seasonality, and a reservoir hosting viruses year-round. The model links the genetic and the epidemiological processes, shaping at nested scales the demogenetic dynamics of viruses.• The choice of the resistance gene (characterized by the equilibrium frequency of the resistance-breaking virus at mutation-selection balance in a susceptible plant) is the most influential leverage of action. Our results showed that optimal strategies of resistance deployment range from 'mixture' (where susceptible and resistant cultivars coexist) to 'pure' strategies (with only resistant cultivar) depending on the resistance characteristics and the epidemiological context (epidemic incidence and landscape connectivity).• We demonstrate and discuss gaps concerning virus epidemiology across the agro-ecological interface that must be filled to achieve sustainable disease management.

We consider a control problem for a single bioreaction occuring in a continuous and well mixed bioreactor, assuming that the bioreaction's kinetics is not represented by a validated model. We develop a nonlinear controller and prove the global asymptotic stability of the closed loop system towards the equilibrium corresponding to the set point. Since this control law needs the knowledge of some parameters, we derive an adaptive version of the nonlinear controller and prove again the global asymptotic stability of the closed loop system. Finally, we show the relevance of our approach on a real life wastewater treatment plant.

The management of genes conferring resistance to plant–pathogens should make it possible to control epidemics (epidemiological perspective) and preserve resistance durability (evolutionary perspective). Resistant and susceptible cultivars must be strategically associated according to the principles of cultivar mixture (within a season) and rotation (between seasons). We explored these questions by modeling the evolutionary and epidemiological processes shaping the dynamics of a pathogen population in a landscape composed of a seasonal cultivated compartment and a reservoir compartment hosting pathogen year-round. Optimal deployment strategies depended mostly on the molecular basis of plant–pathogen interactions and on the agro-ecological context before resistance deployment, particularly epidemic intensity and landscape connectivity. Mixtures were much more efficient in landscapes in which between-field infections and infections originating from the reservoir were more prevalent than within-field infections. Resistance genes requiring two mutations of the pathogen avirulence gene to be broken down, rather than one, were particularly useful when infections from the reservoir predominated. Combining mixture and rotation principles were better than the use of the same mixture each season as (i) they controlled epidemics more effectively in situations in which within-field infections or infections from the reservoir were frequent and (ii) they fulfilled the epidemiological and evolutionary perspectives.

Semi-discrete models are a particular class of hybrid dynamical systems that undergo continuous dynamics most of the time but repeatedly experience discrete changes at some given moments. In the life sciences, since the first semi-discrete model was derived to describe population dynamics by Beverton & Holt (Beverton & Holt 1957 In Fisheries investigations , series 2, vol. 19), a large body of literature has been concerned with such modelling approaches. The aim of the present contribution is twofold. On the one hand, it provides a comprehensive introduction to semi-discrete modelling through two illustrative examples: the classical work by Beverton and Holt is recalled and an original example on immigration in a population model affected by a strong Allee effect is worked out. On the other hand, a short overview of the different applications of semi-discrete models in the life sciences is proposed.

The Marginal Value Theorem (MVT) is a cornerstone of biological theory. It connects the quality and distribution of patches in a fragmented habitat to the optimal time an individual should spend exploiting them, and thus its optimal rate of movement. However, predictions regarding how habitat alterations should impact optimal strategies have remained elusive, with heavy reliance on graphical arguments. Here we derive the sensitivity of realized fitness and optimal residence times to general habitat attributes, for homogeneous and heterogeneous habitats, retaining the level of generality of the MVT. We provide new predictions on how altering travel times, patch qualities and/or relative abundances should affect optimal strategies, and study the consequences of habitat heterogeneity. We show that knowledge of average characteristics is in general not sufficient to predict the change in the average rate of movement. We apply our results to examine the conditions under which the optimal strategies are invariant to scaling. We prove a previously conjectured form of invariance in homogeneous habitats, but show that invariances to scaling are not generic in heterogeneous habitats. We also consider the relative exploitation of patches that differ in quality, clarifying the conditions under which it is adaptive to stay longer on poorer patches.

The coexistence of closely related plant parasites is widespread. Yet, understanding the ecological determinants of evolutionary divergence in plant parasites remains an issue. Niche differentiation through resource specialization has been widely researched, but it hardly explains the coexistence of parasites exploiting the same host plant. Time-partitioning has so far received less attention, although in temperate climates, parasites may specialize on either the early or the late season. Accordingly, we investigated whether seasonality can also promote phenotypic divergence. For plant parasites, seasonality generally engenders periodic host absence. To account for abrupt seasonal events, we made use of an epidemic model that combines continuous and discrete dynamics. Based on the assumption of a trade-off between in-season transmission and inter-season survival, we found through an "evolutionary invasion analysis" that evolutionary divergence of the parasite phenotype can occur. Since such a trade-off has been reported, this study provides further ecological bases for the coexistence of closely related plant parasites. Moreover, this study provides original insights into the coexistence of sibling plant pathogens which perform either a single or several infection cycles within a season (mono- and polycyclic diseases, or uni- and multivoltine life cycles).

This paper deals with the problem of controlling anaerobic digestion processes. A two-step (i.e. acidogenesis-methanization) mass balance model is considered for a 1 m3 fixed bed digester treating industrial wine distillery wastewater. The control law aims at regulating the organic pollution level while avoiding washout of biomass. To this end, a simple output feedback controller is considered which regulates a variable strongly related to the Chemical Oxygen Demand (COD). Numerical simulations assuming noisy measurements first illustrate the robustness of this control procedure. Then, the regulating procedure is implemented on the considered anaerobic digestion process in order to validate and demonstrate its efficiency in real life experiments.

By combining high-throughput sequencing (HTS) with experimental evolution, we can observe the within-host dynamics of pathogen variants of biomedical or ecological interest. We studied the evolutionary dynamics of five variants of Potato virus Y (PVY) in 15 doubled-haploid lines of pepper. All plants were inoculated with the same mixture of virus variants and variant frequencies were determined by HTS in eight plants of each pepper line at each of six sampling dates. We developed a method for estimating the intensities of selection and genetic drift in a multi-allelic Wright-Fisher model, applicable whether these forces are strong or weak, and in the absence of neutral markers. This method requires variant frequency determination at several time points, in independent hosts. The parameters are the selection coefficients for each PVY variant and four effective population sizes Ne at different time-points of the experiment. Numerical simulations of asexual haploid Wright-Fisher populations subjected to contrasting genetic drift (Ne ∈ [10, 2000]) and selection (|s| ∈ [0, 0.15]) regimes were used to validate the method proposed. The experiment in closely related pepper host genotypes revealed that viruses experienced a considerable diversity of selection and genetic drift regimes. The resulting variant dynamics were accurately described by Wright-Fisher models. The fitness ranks of the variants were almost identical between host genotypes. By contrast, the dynamics of Ne were highly variable, although a bottleneck was often identified during the systemic movement of the virus. We demonstrated that, for a fixed initial PVY population, virus effective population size is a heritable trait in plants. These findings pave the way for the breeding of plant varieties exposing viruses to stronger genetic drift, thereby slowing virus adaptation.